Sec theta - Csc theta / (csc theta)(sec theta)

Answer:sin(x)-cos(x)Step-by-step explanation:[tex]\frac{\frac{1}{cos(x)} - \frac{1}{sin(x)}  }{\frac{1}{sin(x)} * \frac{1}{cos(x)}  }[/tex]Simplify the denominator:[tex]\frac{\frac{1}{cos(x)} - \frac{1}{sin(x)}  }{\frac{1}{cos(x)sin(x)}  }[/tex]Simplify the numerator:[tex]\frac{{\frac{2(sin(x)-cos(x))}{sin(2x)} }  }{\frac{1}{sin(x)} * \frac{1}{cos(x)}  }[/tex]Divide the fractions: (a/b)/(c/d) = (a * d)/(b * c):[tex]\frac{(-cos(x)+sin(x))*2cos(x)sin(x)}{sin(2x)}[/tex]Use the identity: 2cos(x)sin(x) = sin(2x):[tex]\frac{sin(2x)(-cos(x)+sin(x))}{sin(2x)}[/tex]Cancel out the common factor (sin(2x)):-cos(x) + sin(x)Simplify:sin(x) - cos(x)